Inexact Proximal Point Methods for Multiobjective Quasiconvex Minimization on Hadamard Manifolds

Erik Alex Papa Quiroz, Nancy Baygorrea Cusihuallpa, Nelson Maculan

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we present two inexact scalarization proximal point methods to solve quasiconvex multiobjective minimization problems on Hadamard manifolds. Under standard assumptions on the problem, we prove that the two sequences generated by the algorithms converge to a Pareto critical point of the problem and, for the convex case, the sequences converge to a weak Pareto solution. Finally, we explore an application of the method to demand theory in economy, which can be dealt with using the proposed algorithm.

Original languageEnglish
Pages (from-to)879-898
Number of pages20
JournalJournal of Optimization Theory and Applications
Volume186
Issue number3
DOIs
StatePublished - 1 Sep 2020
Externally publishedYes

Keywords

  • Hadamard manifolds
  • Multiobjective optimization
  • Pareto optimality
  • Proximal point methods
  • Quasiconvex function

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